Optimal Reinsurance Strategy Under Almost Stochastic Dominance

Comparison of risk is one of the important contents insurance and actuarial,stochastic dominance offered to provide a simple tool to select the optimal risk assets as it is widely applied to the field of decision analysis,portfolio and so on.Almost stochastic dominance is based on stochastic dominance improved on,so that stochastic dominance theory more reasonable.Therefore almost stochastic dominance theory,not only can improve the stochastic dominance theory,and can make more informed decisions on practical problems,resulting in better economic and social benefits.In this paper,for many types of insurance companies have different risks for proportional reinsurance and stop-loss reinsurance,under stochastic dominance and stochastic dominance constraints guidelines almost investigate optimal proportional reinsurance policy issues,the main contents include:(1)By studying stochastic dominance theory and almost stochastic dominance theory,the optimal reinsurance model under stochastic dominance is given,when the random loss is a random variable that follows a discrete distribution,existence theorem to obtain the optimal solution of the problem,and build on the basis of mathematical models and numerical algorithms are given,the advantages and disadvantages of the model.(2)Almost stochastic dominance theory can be regarded as the theory of stochastic dominance conditions relaxed than stochastic dominance theory more realistic situation.In almost stochastic dominance constraints,the optimal reinsurance also becomes a problem of linear programming problem,the same can be obtained existence theorem optimal solution of the problem,and the establishment of mathematical models and numerical algorithms are given based on this analysis the advantages and disadvantages of the model.(3)Optimal model for reinsurance almost stochastic dominance and stochastic dominance constraints by comparing the model can get the optimal reinsurance optimal reinsurance model almost stochastic dominance constraints than stochastic dominance constraints are more advanced and flexibility.Almost random factor plays a decisive role in this model,when almost random coefficient tends to zero,almost stochastic dominance under optimal reinsurance equivalent to the optimal reinsurance under stochastic dominance.By building two types of integrated operator,able to describe most of inducing a linguistic multiple attribute decision-making problems,and provided examples of valid proof of its feasibility and effectiveness in practice.